## Numerical Methods for Partial Differential Equations

This course focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The lectures are intended to accompany the book Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. The contents of this course is suitable for viewers at the graduate level, and is meant to serve as preparatory material for application-specific advanced computational courses such as computational fluid dynamics, computational heat transfer, and computational electromagnetics.

This course focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The lectures are intended to accompany the book Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods.

The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow.

• These lectures along with the book provide a thorough understanding of how to develop computer programs for solving partial differential equations typically encountered in science and engineering from the ground up.
• They demonstrate the finite volume method for unstructured mesh, a method used frequently by practicing code developers in industry.
• And finally include extensive instruction on how to solve a system of linear algebraic equations by iterative methods.

The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses.

### Recommended Reading

Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods
ISBN-13: 978-0128498941
ISBN-10: 0128498943